How do I code Ziegler-Nichols Tuning Method to find PID control constants?

I need to use the Ziegler-Nichols Tuning rules to determine the PID control constants for the following system to meet a settling time ts ≤ 5 sec, an overshoot of Mp ≤ 50%, and zero steady state error to a unit step function input.

System: PID control = Kp((Ti*Td*s^2+Ti*s+1)/(Ti*s))

And plant open loop transfer function = 10/(2*s^3+12*s^2+22*s+12)

PID control and plant function are in series with negative feedback loop.

For PID control tuning rules are as follows, Kp=0.6*Kr, Ti=0.5*Pcr, Td=0.125*Pcr

I appreciate your help.

[kerem]

transfer fonksiyonu verilen bir sistem için PID katsayıları nasıl belirleyebilirim?

[Sam Chak]

Hi @kerem

I suggest posting a new question and providing the transfer function of the given Plant. However, it is important to note that not all types of transfer functions can be stabilized by a PID controller. PID controllers are typically most effective for linear systems of 2nd-order or lower.

Answer 1

[ahmad nouri]

What command should I enter to find the PID coefficients using the Ziegler-Nichols method?